Variable-Radius Circles in Constructive Geometric Constraint Solving Ching-Shoei Chiang Computer and Information Science Soochow University [email protected] Variable-radius circles are common constructs in planar constraint solving and are usually not handled fully by algebraic constraint solvers. We give a complete treatment of variable-radius circles when such a circle must be determined simultaneously with placing two groups of geometric entities. The problem arises for instance in solvers using triangle decomposition to reduce the complexity of the constraint problem. The constraint on the variable-radius circle is the distance to its circumference or its center, and the relative motions on the considered clusters are translational and rotational. This talk covers the summary of three papers. Two papers, cooperated with Professor Christoph Hoffmann, treat the circumference constraints, and the other one, cooperated with Professor Robert Joan-Arinyo, treats the center constraints in geometric constraint solving.